Reliability metrics in an IP network

ABSTRACT

Embodiments of the present invention are directed to characterizing reliability associated with a network. To characterize the reliability, an edge-pair reliability metric is determined for service edge point pairs. An end-to-end reliability metric is computed based on a distribution of the edge-pair reliability metric for the service edge point pairs and a threshold value.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims is a continuation of U.S. patent applicationSer. No. 12/206,414 filed on Sep. 8, 2008, which is incorporated hereinby reference in its entirety.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to reliability metrics for communicationnetworks, and specifically to defining and determining end-to-endreliability metrics for such networks and a service offered over suchnetworks.

2. Brief Discussion of Related Art

Availability estimation in a public switched telephone network (PSTN)typically relies on the concept of a reference connection. The referenceconnection usually consists of a single path through the PSTN from oneend user to another, including the major network segments needed toconnect two telephone subscribers served by two different central officeswitches. A static allocation of end-to-end objectives to differentnetwork segments is used to meet specific availability requirements.This conventional approach is often used for availability standards.

Typically the level of availability is defined in a customer serviceagreement, where the service provider agrees to maintain theavailability at the specified level. For example, in such an agreement,five-9 availability or 99.999% availability is defined as the level ofavailability to be provided. Availability is typically a time averagemeasure based on an amount of time that a reference connection or aspecified part of the network is unavailable for some specified timeperiod.

In reality, end-to-end availability can vary significantly amongdifferent end points. For IP networks, a model of an end-to-endreference path between provider-edge (PE) routers and an associatedreliability model can be developed. However, IP application flows cantake different paths within the network and the reference connectiontypically provides the availability of one route between a pair of PErouters in the core IP network with the assumption that all routes, orat least a large fraction of them, have a similar availability. Theseconsiderations render the concept of a reference connection lesseffective for IP networks.

SUMMARY OF THE INVENTION

In the embodiments of the present invention, reliability associated witha network can be computed. The preferred embodiments of the presentinvention determine a distribution of an edge-pair reliability metricfor service edge point pairs and compute an end-to-end reliabilitymetric based on the distribution of the edge-pair reliability metric forservice edge point pairs and a threshold value. In some embodiment, theend-to-end reliability metric can be computed by dividing the number ofthe edge-pairs that exceed the threshold value by the number of edgepairs in the network. In other embodiments, the end-to-end reliabilitymetric can be computed by identifying a value corresponding to a certainpercentile of the edge-pair reliability distribution.

In some embodiments, a value of an edge-pair reliability metric forprovider service edge point pairs can be determined by determiningpossible paths between the service edge point pairs and calculating areliability of the possible paths. In some embodiments, a distributionof edge-pair reliability can be determined by weighting the edge pairreliability metric based on at least one of the bandwidth of a pathbetween edge-pairs and the amount of traffic between the edge-pairs

In some embodiments, a value of the reliability metric can be determinedbased on a topology of the network, model data, historical data, and/orproduction data. The end-to-end reliability metric can be associatedwith an availability of the network and/or can be associated with anavailability of a service offered over the network, such as a Voice overIP (VoIP) service. Some embodiments of the present invention candetermine whether to incorporate additional nodes/links in the networkto increase the end-to-end reliability based on a value of theend-to-end reliability metric.

Other objects and features of the present invention will become apparentfrom the following detailed description considered in conjunction withthe accompanying drawings. It is to be understood, however, that thedrawings are designed as an illustration only and not as a definition ofthe limits of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is an exemplary IP network, for which reliability metrics can bedefined and computed.

FIG. 2 is a block diagram of a functional architecture of a networkconfigured with an Internet Protocol (IP) Multimedia Subsystem (IMS).

FIG. 3A is a flowchart illustrating a preferred embodiment of thepresent invention.

FIG. 3B is a flowchart illustrating one embodiment for computing anend-to-end reliability metric.

FIG. 4 is an exemplary distribution of an edge-pair reliability forservice edge point pairs.

FIG. 5 is an exemplary computing device for implementing a preferredembodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the embodiments of the present invention, effective management ofInternet protocol (IP) network reliability and of services offered oversuch a network can be achieved by defining reliability metrics thatreflect users' experience. Models can be used to estimate thereliability metrics during design and development of the network and/orthe services implemented over the network, and methods can be developedfor measuring the reliability metrics once the network and/or servicesare deployed so that actual network and/or service reliability metricscan be tracked and managed.

The embodiments of the present invention are directed to an approach foridentifying, specifying, and computing values of reliability metrics,such as availability, defects per million (DPM), and the like forInternet protocol (IP) communication networks and services offered oversuch networks. The reliability metrics are preferably computed on anend-to-end basis, which customers can use to measure, monitor, andvalidate the conformance of providers with their service levelagreements. Those skilled in the art will recognize that other networkperformance metrics such as end-to-end delay can also be determinedusing the preferred embodiments of the present invention.

The preferred embodiments can provide an estimation of a reliabilitymetric for edge-pairs (e.g., Provider Edge router pairs) to provide adistribution that is spatial (concatenation in space), rather thantemporal (aggregation over different time intervals). As an example,using the preferred embodiments of the present invention, availabilityof 99.999%, often referred to as five-9 availability, can becharacterized not as a time average measure of a reference path, but asa fraction of network edge-pairs that meet that level of availability.The preferred embodiments can also identify specific pairs of edges thatmay experience lower availability than required.

A “path”, as used herein, refers to a sequence of nodes and linksthrough which data traverses in a network between provider edge routers.

As used herein, a “node” refers to a device associated with a network,such as a provider edge router, a core router, a call control device,session border controller, customer router, and the like.

As used herein, an “edge-pair reliability metric” refers to a quantityassociated with one or more paths in a network between a service edgepoint pair to identify a characteristic for the service edge point pair,such as a reliability characteristic including a level of availabilityassociated with the service edge point pair. Some examples of edge-pairmetrics include path availability associated with the service edge pointpair (edge-pair), defects per million, and the like. A “service edgepoint” refers a node associated with the edge of the network, such as aprovider edge (PE) router, a session border controller, a customerrouter, and the like.

As used herein, an “end-to-end reliability metric”, such as a networkreliability metric or a service reliability metric, refers to a quantitythat can be determined based on the value of edge-pair metrics for oneor more edge-pairs (i.e. service edge point pairs) in a network.End-to-end reliability metrics provide a measure of characteristics ofthe network, such as a level of reliability of the network, or a measureof characteristics of a service offered over the network, such asavailability of the service. Some examples of an end-to-end reliabilitymetric include availability associated with the network or a serviceoffered over the network, defects per million in the network, and thelike.

As used herein, “availability” refers to a percentage of time a network,an edge-pair, a path in the network, and/or a service provided over thenetwork is operational and/or functional, and “unavailability” refers toan inability to connect to the network, an inability to connect a sourceand a destination, and/or an inability to use a service offered over thenetwork.

FIG. 1 is an exemplary portion of an IP network 100 (hereinafter“network 100”). The network 100 can include nodes, such as provider edge(PE) routers 110 a-l, which can include Session Border Controllers 112,and core routers 120 a-f, the implementation of each being generallyknown to those skilled in the art, which are connected by links, such asa conductive material, fiber optic material, a wireless connection(e.g., radio frequencies, satellite communication), and the like.Customers typically connect to the network 100 via the PE routers 110a-l. For example, a customer router 130 a can connect to the PE router110 a and a customer router 130 b can connect to the edge router 1101 toallow customer routers 130 a-b to communicate with each other and withother customer routers connected to the network 100.

Data packets can be transmitted over the network 100 from one customerrouter to another through the PE routers 110 and core routers 120. ThePE router, through which the data packet enters the network 100, can bereferred to as a source PE router and the PE router, through which thedata packet exits the network, is referred to as a destination PErouter. These data packets include, for example, a destination address,data, and a header. The destination of the data packet is generally acustomer router (e.g., customer routers 130 a-g) and the path that thedata packet travels is generally formed based on the destination. Thenetwork 100 can provide multiple paths between two PE routers (a PErouter pair or edge-pair). In some embodiments, a preferred path betweenPE router pairs can be established such that data packets generallytraverse the preferred path to reach the destination. In theseembodiments, alternate paths may be used when there is a problem withthe preferred path. In other embodiments, the data packets may traverseany one of the paths with substantially equal probability.

In some embodiments, the network 100 can support services, such asvoice-over-IP (VoIP), referred to herein as “data”, and the like. As anexample, VoIP can be supported by one or more call control devices 140,such as IP multimedia subsystems (IMS), to provide an end-to-end IPservice. Although embodiments are discussed with reference to an IMSnetwork configuration and a VoIP service to illustrate an implementationof an end-to-end service, those skilled in the art will recognize thatother network configurations can be implemented to provide end-to-endservices, such as tele- and video-conferencing, electronic commerce, andremote medical services.

FIG. 2 is a block diagram of a functional architecture of an IMSconfiguration 200. IMS is well known to those skilled in the art as anetworking architecture for the delivery of VoIP and other multimediaservices. For a network service implementation that uses IMS, ahorizontal control plane 205 with a set of generic functions can bedefined such that an access network 210 in a user/transport plane 215 isisolated from a service layer 220 in an application plane 225. Thehorizontal architecture provides independence from access technology fornetwork convergence and provides reuse of common functions for multipleapplications. Users can be either wired or wireless and can share theservice infrastructure. The control plane 200 can use a Call SessionControl Function (CSCF) for Session Initiation Protocol (SIP) sessionmanagement and call control, such as call admission and signaling of aVoIP call.

Phases in a VoIP call flow can include a connection phase, a mediaphase, and a tear down phase. In the connection phase, a connection isset up between a calling and called party. In the media phase, codedspeech can be streamed between the connected calling and called parties.In the tear down phase, the connection between the parties is torn downand the resources associated with the call are released. IMSconfigurations can use SIP over IP for signaling in the connection andtear down phases, and a Real-Time Transport Protocol (RTP) over IP forthe media phase. The connection, media, and tear down phases can becarried by the same IP network, although each phase may traverse adifferent subset of elements in the network.

Both SIP and RTP are end-to-end protocols. Hence, the traffic forsignaling and media streaming of a call travels between the SIP phonesat user locations. Typically, Session Border Controllers (SBCs) are usedby service providers to exert control over the traffic. SBCs can bedeployed at network edges, in the signaling and/or media streaming pathsbetween the calling and called parties, to provide signaling security,firewall capability, and policing of media traffic. In some embodiment,the SBCs are implemented within the PE routers of the network. In otherembodiments, the SBCs can be implemented as distinct devices in thenetwork.

FIG. 3A is a flowchart illustrating an embodiment for establishing anend-to-end network reliability metric for an IP network and/or anend-to-end service reliability metric for a service provided over the IPnetwork. To begin, information associated with the network can begathered as input data for deriving a distribution of edge-pairreliability metrics (step 300). The information gathered can includeinformation associated with the network topology, link route miles (orair-mile to route-mile conversion), routing information, nodereliability metrics (e.g., node availability), link failurecharacteristics, redundancy, routing convergence, time to repair, andthe like.

Node reliability metrics, such as node availability, for all types ofedge nodes (e.g., PE routers and/or SBCs) and core nodes (e.g., corerouters), can be obtained from the reliability analysis of a nodal modelbased on various components such as ports, line cards, and processormodules using historical, statistical, and/or measured data. Improvedestimation of node reliability may be done as more field data becomesavailable. In some embodiments, node availability can be derived byassuming a typical 4-hour mean time to restore service (MTTR), or usingactual data for service restoration related to hardware and softwarefailures.

Link failure characteristics include link reliability data, such asfailures in time per mile (FITs/mile). A FIT is a unit of reliability,where 1 FIT=1 failure per billion hours. A simple network model canassume that all links have the same failure rate and a more complexmodel may take into account varying risk levels based on geography andhistory of natural and man-made disasters. Alternatively, theavailability of individual nodes or links can be incorporated in themodel to avoid the simplifying assumption of uniform failurecharacteristics since paths for each PE router pair can be identified,given that the network topology and routing method are known. This canrequire more data and increase the computation time.

Information regarding redundancy, routing convergence, and time torepair can be used when deriving edge-pair reliability. Depending on thedesign of the network, and routing method used, failures can be restoredautomatically, manually, or cause service unavailability until a repairis done. The recovery/repair time can vary from a simple model with acoverage factor, which is the probability that automatic restoration issuccessful, to a detailed model of routing convergence behavior.

Using a combination of the above input data, edge-pair reliability canbe calculated for service edge point pairs in the network, such as PErouter pairs, such that a distribution of the edge-pair reliability isobtained for the possible paths between service edge point pairs (step302). As one example, a service provider may wish to calculate theend-to-end availability of a network or service (e.g., an end-to-endreliability metric). The service provider can identify pairs of PErouters in the network and calculate the availability for the pairs ofPE routers to form a distribution of edge-pair availability (e.g.,edge-pair reliability metric). In some embodiments, high percentiles ofthe edge-pair reliability metric distribution can be used as a metric tocharacterize the overall availability of the network. In this case, thenetwork reliability metric is defined as the availability level so thata specified fraction of the edge pairs have availability exceeding thatlevel. In other embodiments, the approach can weigh the availability ofa path with the bandwidth of its bottleneck link or the availability ofan edge-pair with (actual or forecasted) traffic.

Using the distribution of the calculated edge-pair reliability metricfor the pairs of service edge point pairs, an end-to-end reliabilitymetric (e.g., end-to-end network reliability metric or end-to-endservice reliability metric) for the network, or services provided overthe network, can be calculated based on a number of pairs of PE routersthat achieve a reliability level that is higher than that of a specifiedthreshold value, such as a reliability level specified in a serviceagreement (step 304). The network design can be evaluated to determinewhether desired reliability levels are met (step 306). If the desiredreliability levels, such as a desired level an end-to-end availability,are not met, it can be determined that additional nodes and/or linksneed to be added to the network topology, or redundancy in certain partsof the network needs to be enhanced to achieve these desired objectives.

In some embodiments, an end-to-end reliability metric can be calculatedby dividing the number of service edge pairs that exceed the specifiedvalue by a number of service edge pairs in the network (e.g., a totalnumber of PE router pairs in the network). For example, for end-to-endavailability, the number of PE router pairs that exceed a specifiedavailability value of 99.999% are identified and are divided by thetotal number of PE router pairs to obtain a characterization of theend-to-end availability of a service or network (network reliabilitymetric).

FIG. 3B illustrates one embodiment for calculating an edge-pairreliability and calculating an end-to-end reliability metric based onthe edge-pair reliability metric. To begin, the threshold value isidentified and a number of service edge pairs in the network isidentified, to which a variable M is set (step 310). A counter “Count”and an index “N” of edge-pairs are initiated to zero (step 312).Subsequently, the index N is incremented, the variable M is decremented,and an edge pair reliability metric, such as an edge-pair availability,is calculated based on input data gathered for an edge-pair associatedwith the current value of the index N (step 314). In one embodiment, theedge-pair reliability metric can be calculated using all routers andlinks on the shortest path(s) of an edge-pair.

The calculated edge-pair reliability metric associated with theedge-pair of the current index N is compared to the threshold, and ifthe value of the edge-pair reliability metric exceeds the threshold(step 316), Count is incremented (step 318). Next, the number of pairsof service edge point pairs M is compared to zero (step 320). If thevariable M is greater than zero, the process repeats from step 314 tocalculate the edge-pair reliability for additional edge-pairs.Otherwise, the edge-pair reliability for all edge-pairs is computed, andthe end-to-end reliability metric is calculated by dividing the value ofCount by the value of the index N (step 328).

An embodiment of the present invention is discussed generally withrespect to a VoIP service supported over an IP Multimedia Subsystem(IMS). Some examples of user-oriented metrics to characterize VoIPservice reliability are end-to-end service availability, defects permillion (DPM), and the like. While these embodiments are discussed inrelation to VoIP supported over IP Multimedia Subsystem (IMS) as anend-to-end IP service, those skilled in the art will recognize thatthese embodiments can be implemented for other services and networkimplementations. In addition to failure rates, the end-to-end serviceavailability and DPM also can depend on failure detection time and faultrecovery.

From a VoIP service perspective, users wish to be able to access a voiceapplication, initiate a voice call, continue using the voice applicationwith no interruption, and fulfill the initiated voice call at anacceptable quality. In other words, for a voice call to be completedsuccessfully, the network elements traversed must be in an operationalcondition for the duration of the call. Once the specific subset ofnetwork elements that are used in a call is determined, modeling canthen be developed to establish network objectives so as to meet servicerequirements.

Network elements include links (e.g., connections between nodes, such asfiber optic cable, twisted pair, radio frequency, etc.) and nodes (e.g.routers, SBCs, IMS servers, application servers, and their respectivehardware and software components, such as cards, processors, powersupplies, fans, operating systems, and application-layer software). Theservice reliability of VoIP depends on the reliability of the networkelements that are traversed by the signaling flow and voice path. For aservice end-to-end distribution, the access availability estimates canextend to the user sites at both ends and local networks can be added.

It is expected that the availability objectives of service providers forVoIP can preserve the high level of network reliability currentlyprovided by the public switched telephone network (PSTN). For example,the carrier-grade five-9 availability is typically associated with theClass 4 or Class 5 switches in PSTN. This amounts to a downtime of 5.25minutes/year, or 0.86 seconds/day. End-to-end service availability ofVoIP services usually does not meet the five-9 level. For example, usingthe conventional approach of reference connections, an end-to-end(including local loops) availability of 99.93%, or about 368 minutesdowntime per year can be typical for a single path.

To make the reliability of VoIP over IMS comparable to the PSTN requiresthe availability of IMS network elements to be higher than 99.93%. Thenetwork implementation and element availability can be a determiningfactor in the end-to-end availability (network reliability metric).Higher end-to-end availability can be achieved by IMS element redundancyand network diversity. For example, fully redundant IMS systems aretypically located at two geographically separated sites in the backboneIP network so that when an IMS location is lost, users can be served byIMS core elements at another location.

Since SBCs are placed at network edges, the edge-to-edge unavailabilityof IMS core network connectivity can be tracked in terms of theunavailability for the associated routes connecting the SBCs.Specifically, the edge-pair availability distribution can map directlyto the SBC-to-SBC availability distribution. The high percentiles ofthis distribution can then be used as a metric for the overallavailability of the network. By adding user access availabilityestimates, end-to-end service availability can be derived.

The end-to-end service availability metric may not incorporate customerdemands during outages. The defects per million (DPM) metric can providea direct measure of customer demands that are not served. DPM can becomputed as an average number of blocked calls and cutoff calls permillion of attempted calls. Customer demands can be measured in terms ofthe number of call attempts generated over some time interval. A stablecall, or a call in progress, is a call attempt that has beensuccessfully established. A blocked call is a call attempt that wasprevented from being successfully setup due to failures. A cutoff calloccurs when a stable call is terminated prior to either party going“on-hook,” or the call is abandoned by customer due to perceived poorquality.

As large carriers transport several hundred million calls per day, theDPM calculation can be averaged over a large sample. Like SBC-to-SBCavailability, the preferred embodiments of the present invention can beused to estimate DPM based on the service provider's network topologyrather than using a reference connection. Failure durations affectstable and new calls differently and can be accounted for in thedetermination of the DPM. For example, if the duration of a failure isless than a specific value, then it should not be considered in theestimation of DPM.

By using an edge-pair reliability metric distribution, an advantageousapproach is presented that characterizes IP networks to provide moreinformation on network reliability, such as availability or DPM, acrossan IP network and also advantageously defines and characterizes servicereliability metrics associated with IP network implementations. Althoughavailability and DPM have be used to illustrate the advantages of thepreferred embodiments, those skilled in the art will appreciate that thepreferred embodiments can apply this topology-based approach to deriveother network performance metrics, such as PE-to-PE latency, and thelike.

FIG. 4 illustrates an exemplary distribution 400 of an edge-pairreliability metric for edge-pairs in the network. The exemplarydistribution 400 represents a distribution of the edge-pair reliabilitymetric for edge pairs in a network. The distribution is depicted on agraph where the x-axis corresponds to the complement of availability(i.e., an unavailability level) and the y-axis corresponds to a fractionof PE router pairs. Curve 410 shows unavailability distributionindependent of traffic, while curve 420 shows same with each PE pairweighted proportionally to its forecasted demand obtained from a trafficmatrix.

The exemplary distribution 400 was derived for a network with more than100 PE routers, and in spite of having more than 10,000 PE pairs, therange of values is quite narrow. Two PE nodes, which exist on everypath, contribute the minimum unavailability of 40*10⁻⁶, and the elevatedunavailability due to the additional nodes and links reaches highpercentiles at 50*10⁻⁶ to 60*10⁻⁶, depending on the curve. Thetraffic-weighted curve has lower unavailability since the paths for thehigh-bandwidth PE pairs are the ones with fewer links.

Based on the above observations, instead of average availabilityobjectives of five 9s or four 9s, a network can be characterized interms of a percentage of PE pairs with a given level of availability.Using the exemplary distribution 400, an objective of 99% of the trafficfrom PE pairs with availability of 99.995% or better can be anachievable target for the network of this example. The reliability canbe increased to approach a level of five 9s in this network byincreasing redundancy. For example, the PE router pair availability ofFIG. 4 can improve by implementing access to dual PE routers at thenetwork edge. In this example, dual PE routers on both ends of thenetwork can result in more than 70% of the PE pairs having better thanfive-9 availability.

FIG. 5 depicts an exemplary computing device 500 for establishing and/ordetermining edge-pair reliability metrics of a network and/or serviceoffered over the network and network reliability metrics. The computingdevice 500 can be a mainframe, personal computer (PC), laptop computer,workstation, handheld device, such as a PDA, or the like. In theillustrated embodiment, the computing device 500 includes a centralprocessing unit (CPU) 502 and preferably a display device 504. Thedisplay device 504 enables the computing device 500 to communicatedirectly with an operator through a visual display. The computing device500 can further include data entry device(s) 506, such as a keyboard,touch screen, and/or mouse. The computing device 500 can include storage508 to store data and instructions. The storage 508 can include suchtechnologies as a floppy drive, hard drive, tape drive, Flash drive,optical drive, read only memory (ROM), random access memory (RAM), andthe like. The storage 508 can include applications 510 includinginstructions for implementing those embodiments described herein.

Storage 508 can be local or remote to the computing device 500. Thecomputing device 500 preferably includes a network interface 514 forcommunicating with the network 100. The CPU 502 operates to run theapplications 510 in storage 508 by performing instructions therein andstoring data resulting from the performed instructions, which may bepresented to a user via the display 504 or by other mechanisms known tothose skilled in the art, such as via a printer. The data can include avalue for one or more reliability metrics for network, service, path,and/or element reliability.

Although preferred embodiments of the present invention have beendescribed herein with reference to the accompanying drawings, it is tobe understood that the invention is not limited to those preciseembodiments and that various other changes and modifications may beaffected herein by one skilled in the art without departing from thescope or spirit of the invention, and that it is intended to claim allsuch changes and modifications that fall within the scope of theinvention.

What is claimed is:
 1. A method of determining reliability associatedwith a network comprising: determining, using a processing device, aquantity of edge-pairs associated with the network having an edge-pairreliability metric value that satisfies a reliability requirement; andcomputing, using the processing device, an end-to-end reliability metricrepresenting the reliability associated with the network, includingdividing the quantity of edge-pairs for which the edge-pair reliabilitymetric value satisfies the reliability requirement by a total quantityof edge-pairs associated with the network.
 2. The method of claim 1,wherein the reliability requirement is satisfied when the edge-pairreliability metric value exceeds a threshold value.
 3. The method ofclaim 1, further comprising determining the edge-pair reliability metricbased on a topology of the network.
 4. The method of claim 1, furthercomprising determining the edge-pair reliability metric value forservice edge point pairs by determining possible paths between theedge-pairs and calculating a reliability of the possible paths.
 5. Themethod of claim 1, wherein the reliability requirement represents anavailability of the network.
 6. The method of claim 1, wherein thereliability requirement represents an availability of a service offeredon the network.
 7. The method of claim 6, wherein the service includes avoice-over-Internet protocol service.
 8. The method of claim 1, furthercomprising determining whether to incorporate at least one of additionalnodes and links associated with the network based on a value of theend-to-end reliability metric.
 9. The method of claim 1, furthercomprising determining a distribution by weighting the edge-pairreliability metric value based on at least one of a bandwidth of a pathbetween edge-pairs and the quantity of traffic between edge-pairs. 10.The method of claim 1, wherein determining the quantity of edge-pairs inthe network that have the edge-pair reliability metric value thatsatisfies the reliability requirement comprises comparing the edge-pairreliability metric value associated with each of the edge-pairs to athreshold value.
 11. An apparatus to determine reliability associatedwith a network comprising: a processing device; and a computer-readablemedium to store instructions, that when executed by the processingdevice, cause the processing device to perform operations comprising:determining a quantity of edge-pairs associated with the network havingan edge-pair reliability metric value that satisfies a reliabilityrequirement; and computing an end-to-end reliability metric representingthe reliability associated with the network, including dividing thequantity of edge-pairs for which the edge-pair reliability metric valuethat satisfies the reliability requirement by a total quantity ofedge-pairs associated with the network.
 12. The apparatus of claim 11,wherein the reliability requirement is satisfied when the edge-pairreliability metric value exceeds a threshold value.
 13. The apparatus ofclaim 11, wherein the operations further comprise computing whether toincorporate at least one of additional nodes and links associated withthe network based on a value of the end-to-end reliability metric. 14.The apparatus of claim 1, wherein the operations further comprisecomputing a distribution by weighting the edge pair reliability metricvalue based on at least one of a bandwidth of a path between edge-pairsand a quantity of traffic between the edge-pairs.
 15. The apparatus ofclaim 11, wherein determining the quantity of edge-pairs in the networkthat have the edge-pair reliability metric value that satisfies thereliability requirement comprises comparing the edge-pair reliabilitymetric value associated with each of the edge-pairs to a thresholdvalue.
 16. A computer-readable storage medium to store instructionsthat, when executed by a processing device, cause the processing deviceto perform operations comprising: determining a quantity of edge-pairsassociated with the network having an edge-pair reliability metric valuethat satisfies a reliability requirement; and computing an end-to-endreliability metric representing the reliability associated with thenetwork, including dividing the quantity of edge-pairs for which theedge-pair reliability metric value satisfies the reliability requirementby a total quantity of edge-pairs associated with the network.
 17. Thecomputer-readable storage medium of claim 16, wherein the reliabilityrequirement is satisfied when the edge-pair reliability metric valueexceeds a threshold value.
 18. The computer-readable storage medium ofclaim 16, wherein determining the quantity of edge-pairs in the networkthat have the edge-pair reliability metric value that satisfies thereliability requirement comprises comparing the edge-pair reliabilitymetric value associated with each of the edge-pairs to a thresholdvalue.